A variety of elongate medical device bodies, for example, drug delivery catheters and medical electrical leads, are known in the art, for example, to couple a therapy delivery generator and/or diagnostic device to a target site within a body of a patient, for example, in the spinal column or in any of a number of internal organs. Those skilled in the art are familiar with various apparatus and methods for anchoring these implanted device bodies. FIG. 1 is a schematic depicting a surgical incision site 12 through which an exemplary elongate medical device body 110 has been implanted. FIG. 1 illustrates a length of device body 110 extending proximally out from site 12, and an anchor apparatus 10 surrounding device body 110 to facilitate anchoring of device body 110 to subcutaneous tissue 14, for example, via sutures (not shown) tied thereabout and sewn into the tissue 14. Anchor apparatus 10, for example, configured as a silicone sleeve, can provide a protective interface between sutures and device body 110, when the sutures are secured around device body 110 to prevent movement of body 110 relative to both apparatus 10 and the tissue anchoring site. However it may be preferable that an anchor apparatus be configured to provide a uniform, even compression around body 110, which prevents movement of body 110 relative to the anchor apparatus, without the sutures. Tools for deploying such an anchor apparatus onto device bodies are known in the art, yet there is still a need for new apparatus and methods for tissue anchoring of medical devices.